Why the Ferrite in an air gapped core?

In a comment to the video:

“The gap in inductors’ core: a different (interesting) perspective”
https://youtu.be/CCS_sPgb6U4

Prof. Slobodan Cuk wrote:

“….minute air-gaps of 1mm or less effectively “kill” the inductance by a factor of 100 to a 1000 to the point that ferrite cores used are completely wasted as they contribute only core losses and large extra weight! In fact, the ferrite core is only there to define the length of the air-gap and with that the uktra (ultra?) low inductance!?”

Видео Why the Ferrite in an air gapped core? канала Sam Ben-Yaakov